iCloud Lock Removal is the most difficult category of iPhone Unlocking. In order to remove the iCloud Lock from an iPhone, you will have to contact Apple Support or the original owner.
By original owner (or Previous owner) we mean the person whose Apple ID and Password got you stuck on the Activation Screen.
Since removing the iCloud Lock from an iPhone, iPad or iPod Touch is a very difficult procedure with low success rate, the best solution is to pre-check an iDevice before buying it!
That way you will not get into this unfortunate situation, of trying to get in touch with Apple or the Previous owner, and requesting an iCloud Lock Removal.
The situation is more difficult when an iPhone is iCloud Locked and reported as LOST. Those cases do not have a solution :S
Find out how to make a formal iCloud Lock Removal request to Apple (The iCloud Support Department) and how to find the original owner of an iCloud Locked iPhone and negotiate with him.